The Solve(ODE, y(x)) command finds the solution of an ordinary differential equation.

Student[ODEs][Solve] is also a subpackage containing a number of commands for solving ordinary differential equations and systems of ODEs.

Each command in the Student[ODEs][Solve] subpackage can be accessed by using either the long form or the short form of the command name in the command calling sequence.

The long form, Student[ODEs][Solve]:-command or Student:-ODEs:-Solve:-command, is always available. The short form can be used after loading the package.

The Maple Command Completion facility is helpful for entering the names of Student package commands.

The subpackage Student[ODEs][Solve] consists of commands for solving ODEs and systems according to various methods:

To display the help page for a particular Student[ODEs][Solve] command, see Getting Help with a Command in a Package.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{ODEs}\right]\right)\:$

$\mathrm{ode1}≔t^2\left(z\left(t\right)+1\right)+{z\left(t\right)}^2\left(t-1\right)\mathrm{diff}\left(z\left(t\right)\,t\right)=0$

$\mathrm{ode1}≔t^2\left(z\left(t\right)+1\right)+{z\left(t\right)}^2\left(t-1\right)\left(\frac{\ⅆ}{\ⅆt}z\left(t\right)\right)=0$

$\mathrm{Solve}\left(\mathrm{ode1}\,z\left(t\right)\right)$

$\frac{{z\left(t\right)}^2}{2}-z\left(t\right)+\ln \left(z\left(t\right)+1\right)=-\frac{t^2}{2}-t-\ln \left(t-1\right)+\mathrm{\_C1}$

$\mathrm{ode2}≔\mathrm{diff}\left(y\left(x\right)\,x\,x\right)-\mathrm{diff}\left(y\left(x\right)\,x\right)-x\exp \left(x\right)=0$

$\mathrm{ode2}≔\frac{{\ⅆ}^2}{\ⅆx^2}y\left(x\right)-\frac{\ⅆ}{\ⅆx}y\left(x\right)-x{\ⅇ}^x=0$

$\mathrm{Solve}\left(\mathrm{ode2}\,y\left(x\right)\right)$

$y\left(x\right)=\mathrm{\_C1}+\mathrm{\_C2}{\ⅇ}^x+\frac{{\ⅇ}^x\left(x^2-2x+2\right)}{2}$

$\mathrm{ode3}≔\mathrm{diff}\left(y\left(x\right)\,x\,x\right)+\frac{5{\mathrm{diff}\left(y\left(x\right)\,x\right)}^2}{y\left(x\right)}=0$

$\mathrm{ode3}≔\frac{{\ⅆ}^2}{\ⅆx^2}y\left(x\right)+\frac{5{\left(\frac{\ⅆ}{\ⅆx}y\left(x\right)\right)}^2}{y\left(x\right)}=0$

$\mathrm{Solve}\left(\mathrm{ode3}\,y\left(x\right)\right)$

$\left\{y\left(x\right)={\left(6{\ⅇ}^{\mathrm{\_C1}}x+6\mathrm{\_C2}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$6$}\right.}\,y\left(x\right)=-{\left(6{\ⅇ}^{\mathrm{\_C1}}x+6\mathrm{\_C2}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$6$}\right.}\right\}$

$\mathrm{ode4}≔x^3\mathrm{diff}\left(y\left(x\right)\,x\,x\,x\right)+3x^2\mathrm{diff}\left(y\left(x\right)\,x\,x\right)-6x\mathrm{diff}\left(y\left(x\right)\,x\right)-6y\left(x\right)=0$

$\mathrm{ode4}≔x^3\left(\frac{{\ⅆ}^3}{\ⅆx^3}y\left(x\right)\right)+3x^2\left(\frac{{\ⅆ}^2}{\ⅆx^2}y\left(x\right)\right)-6x\left(\frac{\ⅆ}{\ⅆx}y\left(x\right)\right)-6y\left(x\right)=0$

$\mathrm{Solve}\left(\mathrm{ode4}\,y\left(x\right)\right)$

$y\left(x\right)=3\mathrm{\_C2}{x}^3-\frac{\mathrm{\_C3}}{x}-\frac{2\mathrm{\_C1}}{x^2}$

The Student[ODEs][Solve] package was introduced in Maple 2021.

For more information on Maple 2021 changes, see Updates in Maple 2021.